A note on the likelihood and moments of the skew-normal distribution.

Eliseo Martínez; Héctor Varela; Héctor W. Gómez; Heleno Bolfarine

SORT (2008)

  • Volume: 32, Issue: 1, page 57-66
  • ISSN: 1696-2281

Abstract

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In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.

How to cite

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Martínez, Eliseo, et al. "A note on the likelihood and moments of the skew-normal distribution.." SORT 32.1 (2008): 57-66. <http://eudml.org/doc/42040>.

@article{Martínez2008,
abstract = {In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.},
author = {Martínez, Eliseo, Varela, Héctor, Gómez, Héctor W., Bolfarine, Heleno},
journal = {SORT},
keywords = {skew-normal distribution; maximum likelihood equations; moments},
language = {eng},
number = {1},
pages = {57-66},
title = {A note on the likelihood and moments of the skew-normal distribution.},
url = {http://eudml.org/doc/42040},
volume = {32},
year = {2008},
}

TY - JOUR
AU - Martínez, Eliseo
AU - Varela, Héctor
AU - Gómez, Héctor W.
AU - Bolfarine, Heleno
TI - A note on the likelihood and moments of the skew-normal distribution.
JO - SORT
PY - 2008
VL - 32
IS - 1
SP - 57
EP - 66
AB - In this paper an alternative approach to the one in Henze (1986) is proposed for deriving the odd moments of the skew-normal distribution considered in Azzalini (1985). The approach is based on a Pascal type triangle, which seems to greatly simplify moments computation. Moreover, it is shown that the likelihood equation for estimating the asymmetry parameter in such model is generated as orthogonal functions to the sample vector. As a consequence, conditions for a unique solution of the likelihood equation are established, which seem to hold in more general setting.
LA - eng
KW - skew-normal distribution; maximum likelihood equations; moments
UR - http://eudml.org/doc/42040
ER -

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